Gauge - invariant fluctuations of the metric in stochastic inflation

Abstract

I derive the stochastic equation for the perturbations of the metric for a gauge - invariant energy - momemtum - tensor (EMT) in stochastic inflation. A quantization for the field that describes the gauge - invariant perturbations for the metric is developed. In a power - law expansion for the universe the amplitude for these perturbations on a background metric could be very important in the infrared sector.